Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$5.50$, and bags of cookies cost $$3.00$, and sales equaled $$52.00$ in total. There were $6$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Solution: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5.5x+3y = 52}$ ${y = x+6}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+6}$ for $y$ in the first equation. ${5.5x + 3}{(x+6)}{= 52}$ Simplify and solve for $x$ $ 5.5x+3x + 18 = 52 $ $ 8.5x+18 = 52 $ $ 8.5x = 34 $ $ x = \dfrac{34}{8.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+6}$ to find $y$ ${y = }{(4)}{ + 6}$ ${y = 10}$ You can also plug ${x = 4}$ into $ {5.5x+3y = 52}$ and get the same answer for $y$ ${5.5}{(4)}{ + 3y = 52}$ ${y = 10}$ $4$ bags of candy and $10$ bags of cookies were sold.